2002/07/31 by J. H. Conway, N. J. A. Sloane
Mathematics · #math.CO #msc:11H31
published as J. Number Theory, 72 (1998), 357-362 · 8 pages
arxiv created 2002/07/31 · arxiv updated 2009/11/30
The highest possible minimal norm of a unimodular lattice is determined in dimensions n <= 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8*1020 in dimension 33). Unimodular lattices with no roots exist if and only if n >= 23, n not = 25.